Three mean-field models for bimolecular reactions proceeding on planar supported catalysts

Abstract

The kinetics of A 1 + A 2 → A 1 A 2 reaction on supported catalysts is investigated numerically using three phenomenological models. The first of them is based on PDEs and includes: the bulk diffusion of both reactants from a bounded vessel towards the adsorbent and the product bulk one into the same vessel, adsorption and desorption of molecules of both reactants, and surface diffusion of adsorbed particles described by the diffusion flux based on the particle jumping into a nearest vacant adsorption site. The second model based on the ODEs is derived by averaging of the first one. The third mixed model is based on the PDEs for the bulk diffusion of both reactants and ODEs for the adsorbates surface diffusion on the supported catalyst which is composed of the active in reaction catalyst particle and inactive support. All three models are solved numerically and their results are compared. Two distinct arrangements of the adsorption sites are used for numerical calculations: (i) concentrations of the adsorption sites of the catalyst particle and support are equal, (ii) the total amount of adsorption sites of the active and inactive in reaction surface parts are the same. Calculations are performed for the case where: (i) molecules of both reactants adsorb only on the support and (ii) particles of one reactant adsorb on the active part while molecules of the other one adsorb on the support. The influence of the surface diffusivity, jump rate constants of the escaped particles of both adsorbates via the catalyst-support interface, and size of the active catalyst particle (or size-dependent distribution of active sites in the second case of their arrangement) on the catalytic reactivity of the supported catalyst is studied.

Mean field treatment of heterogeneous steady state kinetics

“…To circumvent this issue, other groups have introduced an inhomogeneity factor, effectively allowing for local variations in species occupancy probabilities within the mean field approximation. [56,57,58,59,60] However, this approach also differs from our MFSS that finds self consistent steady state populations of species subject to inhomogeneous chemical activity.…”

“…We intentionally build a model as simple as possible, for example ignoring the diffusion of adsorbed H 2 , as is commonly done in method development studies of chemical kinetics. [56,58,60] The diffusion of adsorbed hydrogen is effectively accounted for by the sequence of desorption and adsorption steps (slow diffusion limit). At steady state, these macroscopic rate expressions imply that the rate of production of H 2 gas would be…”